Transcript The Market - Supply & Demand

The Market
Supply & Demand & all that
The Big Picture
P
P
Q
Demand
Supply
Q
P
Equilibrium Price &
Quantity
The Market
Q
Demand


Analysis based on individuals' behavior, then
summing of individuals into aggregate demand at
various prices
Explanations

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
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Verbal: quantity demanded changes inversely w/price
Simple graph: downward sloping curve of P vs Q
Graphic derivation: from preferences
Mathematical specification: D = f(P)
Axiomatic derivation
Indifference Curves - I
Two space defines various combinations of Q1 & Q2
that you might choose. Some (Q1, Q1) you prefer to others,
some you prefer less, some alternatives leave you indifferent.
I1 < I2 < I3
Quant.
of
Good
2
Dem.
(Q2)
An “indifference curve” is defined by set of combinations
among which you are indifferent.
higher levels of preference
higher levels of utility
O
q" q'
q
P1
Quantity of Good 1 Demanded (Q1)
NB: under usual assumptions:
1. Q1 and Q2 are infinitely divisible, so: infinite # of smooth curves
2. curves are open, I.e., you always prefer MORE of everything
Indifference Curves - II
I1 < I2 < I3
Quant.
of
Good
2
Dem.
(Q2)
O
q" q'
q
P1
Quantity of Good 1 Demanded (Q1)
NB: if you drop the assumption that you always prefer
MORE of everything, then at some point curves close,
and MORE would mean a lower level of utility
Budget Line - I
Available budget (money) = M
with prices of Q1 = P1, Q2 = P2
so, total expenditure = M = P1Q1+P2Q2
which defines the “budget line.”
Q2
q2
If all M spent on Q2 then you would be at q2.
If all M spent on Q1 then you would be at q1.
NB: if you spend less than M, you will be at some point
under the budget line in the space defined by 0,q1,q2.
O
q1
Q1
If you rewrite M = P1Q1+P2Q2 as Q2 = (1/ P2)M - (P1 / P2) Q1
you can see that the slope of the line = P1/ P2 (and is negative)
Budget Lines - II
If income (M) increases, budget line shifts right
Q2
M' =P1Q1+P2Q2
M=P1Q1+P2Q2
O
P1
If M' > M, then line shifts right.
Q1
Budget Lines - III
If P1 increases, budget line intercept shifts left
Q2
If P1 increases, max Q1 falls
(Change in P1 would have no effect on
vertical intercept if all M spent on Q2)
O
Q1
If P1<P1’, then intercept shifts left. If P2/P1 changes, slope changes
Utility Maximization
I3
Q2
M=P1Q1+P2Q2
O
q
Q1
To Maximize utility you will want to be on highest possible I.
Highest possible I will be that which is tangent to budget line.
Graphic Derivation of Demand Curve
Demand Curve shows what happens to quantity demanded as price
changes. So we raise P1 and see what happens to Q1
I1 < I2 < I3
P1 "
P1 '
P1 '
P1
P1
P1 "
O
q" q'
q" q'
q
q
Quantity of Good 1 Demanded (Q1)
As price rises, P1< P1'< P1”, quantity demanded falls, q to q’ to q”
and the combinations of P1 and q define a demand curve for Q1.
Mathematical Specification
of Demand Curves
D = f(P)
dD/dP < 0
D/P < 0
Linear Demand Functions
D = a - bP
D = 300 - 20P
Axiomatic Derivation
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Subset of Assumptions
 A > B, A < B, A = B
 axiom of transitivity
 axiom of asymmetry
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comparability
egotism, no one else's consumption matters to you
continuity (continuous curves, eg., indifference curves
insatiability (no maximium, always want more)
Utility
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Indifference Curves defined by:
 preference - further from origin prefered
 utility - further from origin, higher utility
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Utility = satisfaction derived from consumption
Utility derived from "utilitarians" - Eng. Philos.
 all action taken with view to utility to be derived
 measured by "utils"cardinality
 law of diminishing marginal utility (maybe!)
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Utility functions: U = f(x1, x2, .... xn)
Problem w/utility

Cardinality
  you can compare utility for different people
 interpersonal comparisons
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Law of Diminishing Mar. Utility
  how much utility depended upon how much you
have
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Cardinality + Law of Diminishing Utility
  total social utility would increase through
redistribution of money from rich to poor
  a political problem! Solution: shift to ordinality( ±)
  utility theory replaced by preference theory
Supply
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
Analysis based on each firm's behavior, then
summing of firms into aggregate supply at various
prices
Explanations





Verbal: quantity supplied changes directly w/price
Simple graph: upward sloping curve of P vs Q
Graphic derivation: from costs + profit maximization
Mathematical specification: S = f(P)
Axiomatic derivation
Costs
Price, costs
Marginal cost (MC)
average cost
price given
=
marginal revenue
(MR)
quantity produced
Profit Maximization occurs where MC = MR
Derivation of Supply Curve
Price, costs
Marginal cost (MC) = S
P3
P2
P1
q1
q2
Profit Maximization occurs where MC = MR
q3
quantity produced
Mathematical Specification
S = f(P)
dS/dP > 0
S/P > 0
Linear Supply Functions
S = a + bP
S = 300 + 20P
Axiomatic Derivation


Subset of axioms
Existence of Production
 There exists some attainable element x that can be
transformed into y
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Neutrality of Transformations
 any two transformations T are indifferenttheir
inputs are indifferent and their outputs are indifferent

Convexity
 Production set Yj is convex
Change in Technology

Improvements in Technology that lower costs of
production, shift MC curve down, and Supply
curve to Right
MC/S
MC'/S'
Supply shifts
to the right
marginal cost
shifts down
Equilibrium

Shapes of S & D guarantee "equilibrium", i.e.,
tendency to return to price that equalizes them
Supply
P
excess supply
equilibrium price
Demand
equilibrium quantity
Q
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